| M／M／1排队系统嵌入Markov链瞬态解的格路径算法 |
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| 引用本文： | 刘海宁,屈明双. M／M／1排队系统嵌入Markov链瞬态解的格路径算法[J]. 兰州交通大学学报, 2009, 28(4): 151-153 |
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| 作者姓名： | 刘海宁 屈明双 |
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| 作者单位： | 兰州交通大学数理与软件工程学院,甘肃兰州,730070 |
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| 摘 要： | 在定义了生灭过程状态转移的单格与升降格和降升格的基础上，证明了M／M／1排队系统{X（t）t≥0}的嵌入Markov链{X（n），l≥0}的转移概率弱收敛于系统的瞬态解，并利用随机游动的格路径算法求出了该链的转移概率P（i，j，n）的显式算法表达式，从而达到确定M／M／1排队系统{x（t）f≥0}瞬态解的转移概率的目的．
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| 关 键 词： | M/M/1排队系统 瞬态解 转移概率 格路径算法 |
The Lattice Path for Embedded Markov Chain of M/M/1 Queuing System |
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| LIU Hai-ning,QU Ming-shuang. The Lattice Path for Embedded Markov Chain of M/M/1 Queuing System[J]. Journal of Lanzhou Jiaotong University, 2009, 28(4): 151-153 |
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| Authors: | LIU Hai-ning QU Ming-shuang |
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| Affiliation: | (school of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China) |
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| Abstract: | The single lattice,UD-lattice and DU-lattice can be defined with respect to the state transition of birth and death process, and the transition function of embedded Markov chain （X（n）n≥0} convergence in the weak sense to transient solution of the process {X（t）t≥0} for M/M/1 queuing system has been verified. Lattice path for random walk also has been used to obtain the exact representation of transition function P（i,j, n） for embedded Markov chain of M/M/1 queuing system. The aim for transient solution of M/ M/1 queuing system is determined through transition function P（i,j,n） of embedded Markov chain {X（n） n≥0 }. |
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| Keywords: | M/M/1 queuing system transient solution transition function lattice path |
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